Download Linear Algebra

Linear Algebra
MONDAY, AUGUST 11
Learning Goal Focus 1
I
will understand transformations and
use informal arguments to prove
congruency between images using
physical models, transparencies or
geometry software.
Learning Scale
4
In addition to level 3.0
and above and
beyond what was
taught in class, I may:



Make
connection with
real-world
situations
Make
connection with
other concepts
in math
Make
connection with
other content
areas.
3
I will understand
transformations and
use informal
arguments to prove
congruency between
images using physical
models,
transparencies or
geometry software.


explain the
relationship of
the angles
formed when
parallel lines are
cut by a
transversal
justify the
transformation
sequence
between two
congruent
figures
2
I will understand
transformations and
identify congruency
between images
using physical models,
transparencies or
geometry software.




use vocabulary
& find missing
angles
associated with
parallel lines cut
by a transversal
verify the
properties of
rotations,
reflections, &
translations
identify the rigid
transformation
sequence
between two
congruent
figures
write statements
of congruency
1
With help from the
teacher, I have
partial success with
transformations.
0
Even with help, I have no
success with
transformations.
Today’s Learning Target
Target 1:
Students will understand what is meant by a
learning goal, learning target and a learning
scale.
What is a learning goal, learning
scale and learning target?

Discuss with your partner.

Share what you came up

Difference between learning goal and learning target

Learning scale
Why do we have learning goals
and scales?

Discuss with your partner

Important to reflect on our learning

How does reflecting on our learning help us?
Rate your learning using the scale
provided
Level 4
In addition to level 3.0 and above and beyond what was taught in class, I may:



Make connection with real-world situations
Make connection with other concepts in math
Make connection with other content areas.
Level 3
I will understand transformations and use informal arguments to prove congruency between
images using physical models, transparencies or geometry software.


explain the relationship of the angles formed when parallel lines are cut by a transversal
justify the transformation sequence between two congruent figures
Rate your learning using the scale
provided
Level 2
I will understand transformations and identify congruency between images using physical
models, transparencies or geometry software.




use vocabulary & find missing angles associated with parallel lines cut by a transversal
verify the properties of rotations, reflections, & translations
identify the rigid transformation sequence between two congruent figures
write statements of congruency
Level 1
With help from the teacher, I have partial success with transformations.
Level 0
Even with help, I have no success with transformations
Summarize

Who can define a learning goal, learning scale and learning target?

Why is it important to reflect on our learning?
Today’s Learning Target
Target 2
I will define symmetry, a basic design
element, reflectional symmetry, a line of
symmetry, a transformation and a line of
reflection.
Symmetry and Transformations

Symmetry is when one shape becomes exactly like another if you
flip, slide or turn it.

Transformation – A geometric operation that relates each point of a
figure to an image point.
The transformations we will study in this investigation – reflections,
rotations and translations – are “symmetry” translations.

Symmetry translation – produces an image that is identical in size
and shape to the original figure
Basic Design Element

Basic design element - A part of a pattern or design that, when
transformed using at least one type of symmetry transformation will
produce the entire design.
What is the basic design element of the butterfly design?
Where is the line of symmetry?
What is the basic
design element for the
wallpaper design?
What is the direction
and distance of the
translation?
What is the basic design element of the pinwheel design?
How many copies do you need to complete the symmetric design?
Where is the center of rotation?
1.1 Butterfly Symmetry

Reflectional symmetry – A figure or design has reflectional symmetry
if you can draw a line that divides the figure into halves that are
mirror images.

Line of symmetry – The line that divides the figure into halves.

Reflectional symmetry is sometimes referred to as mirror symmetry or
line symmetry.

The design below has reflectional symmetry about a vertical line
through its center.
Line reflection

Line reflection - The geometric operation or transformation that
“flips” a figure and matches each point to an image point.

To identify the image of a point P, you can use prime notation (P’).
You read P’ as “ P prime”.
Summarize
Did we define…..

Symmetry

Basic design element

Reflectional symmetry

Line of symmetry

Transformation

Line of reflection
Rate your understanding
Rate your understanding
Learning Target
I will define symmetry, a basic design
element, reflectional symmetry, a line
of symmetry, a transformation and a
line of reflection.
Learning target
I will understand that a figure
has “flip” or reflectional
symmetry and how each point
is related to its image under
transformation by reflection.
Problem 1.1 A
We need to a ruler and protractor
Problem 1.1 A
Problem 1.1 B
Problem 1.1 C
Problem 1.1 C – Summarize our
Learning
• The line segments we create J
to J’, K to K’, L to L’ and M to M’
are all perpendicular to the
line of reflection
• The line segments we create
are all parallel to each other
• The points (vertices) J and J’
are of equal distance from the
line of reflection.
Rate your understanding
I will understand that a figure
has “flip” or reflectional
symmetry and how each point
is related to its image under
transformation by reflection.
Homework tonight

NONE! 